Alfvén eigenmodes (AE) degrade fast-ion confinement in high β N , steady-state scenarios 5 W.W. (Bill) Heidbrink 1 Amplitude with J. Ferron, 2 C. Holcomb, 3 M. Van Zeeland 2 , E. Bass 4 , X. Chen 2 , C. Collins 1 , A. Garofalo 2 , X. Gong 5 , N. AE Gorelenkov 6 , B. Grierson 6 , C. 0 Petty 2 , M. Podestà 6 , D. Spong 7 , 250 L. Stagner 1 , Y. Zhu 1 ~ Fast-ion Transport 200 Fast-Ion Div.Flux 1 University of California, Irvine 150 2 General Atomics 3 Lawrence Livermore National 100 Laboratory 4 University of California, San Diego 50 5 Institute of Plasma Physics Chinese Academy of Science 0 6 Princeton Plasma Physics Laboratory -50 7 Oak Ridge National Laboratory 2 4 6 8 10 P NBI (MW)
Steady-state Advanced Tokamak (AT) scenarios often have elevated values of safety factor q • Projections predict a stable β N =5 steady-state scenario in DIII-D with increased ECCD and off-axis NBI 1) Poli, NF 54 (2014) J.M. Park, APS (2013) 2) Garofalo, NF 54 (2014) 3) Kessel, FED 80 (2006)
Many DIII-D discharges with q min >2 have poor global confinement Uses Thermal + Fast Ion Stored Energy 2.6 Is degraded fast- ( 2.7 < N < 3.9, 4.5 < q 95 < 6.8) ion confinement H 89 = E 2.4 the culprit? 89 2.2 Typical H- 2.0 mode level 1.8 1.6 1.5 2.0 2.5 1.0 q min Ferron, PoP 20 (2013) 092504
Outline 1. AEs degrade fast-ion confinement in many steady-state scenario discharges 2. Degradation of fast-ion confinement can account for the overall degradation in global confinement 3. Physical mechanism of fast-ion transport: critical gradient behavior due to many wave- particle resonances 4. Outlook
Use TRANSP to quantify the degradation in fast-ion signals (10 15 n/s) #154406 • Use spatially uniform 1.2 C lassical P rediction ad hoc fast-ion 0.8 ONS diffusion D f in TRANSP 0.4 M easured S UTR as an empirical Variable D f P rediction ignal NE measure of 0.0 degraded fast-ion (b) S ignal /C 3 lassical 1.0 confinement 2 0.67 • Alternatively, use Variable D f (m 2 /s) 1 0.33 ratio of signal to 0 0 “classical” prediction 2.4 onfinement “H89” (c) G lobal C • Global confinement 2.0 varies with fast-ion 1.6 confinement 1.2 2 3 4 5 6 TIME ( s )
The qmin~2 discharge has more AEs and worse confinement than the qmin~1 discharge
Many Alfvén Eigenmodes are Observed & Expected Calculated Unstable TAE Measured Simultaneous Modes #152932 @ 2.962 s (a) 113 k Hz 10 (ECE) Amp (eV) 8 6 4 2 0 20 (b) 137 kHz Amp (eV) 15 GYRO 10 5 0 10 (c) 153 kHz Amp (eV) 8 6 4 2 0 0.2 0.4 0.6 0.8 1.0 MINOR R ADIUS Typical toroidal mode numbers: 2-5
q min ~1 data agree with predicted fast-ion signals qmin ~ 1 FIDA (10 16 ph/s-sr-m 2 ) 2.0 Classical 1.0 0 180 200 220 MAJORR ADIUS (cm) Ratio of signal to calculated predictions Classical Neutrons 89% W f ast 100%
q min ~1 data agree with predicted fast-ion signals but q min ~2 data do not qmin ~ 2 qmin ~ 1 FIDA (10 16 ph/s-sr-m 2 ) 2.0 1.0 0 180 200 220 MAJORR ADIUS (cm) Ratio of signal to calculated predictions * Classical Classical Neutrons 89% 61% W f ast 100% 72%
Assuming fast-ion diffusion of 1.3 m 2 /s gives approximate agreement with qmin~2 data Ratio of signal to calculated predictions W f ast 100% 72% 108% * Classical Classical D f Neutrons 89% 61% 91%
Degraded fast-ion signals correlate with increasing Alfvén eigenmode activity • Every diagnostic that is sensitive to co-passing fast ions measures reductions • The “AE Amplitude” is the average amplitude of coherent modes in the TAE band (from interferometer signals) • Data from quasi- stationary portion of steady-state scenario discharges
Outline 1. AEs degrade fast-ion confinement in steady- state scenario discharges 2. Degradation of fast-ion confinement can account for the overall degradation in global confinement 3. Physical mechanism of fast-ion transport: critical gradient behavior due to many wave- particle resonances 4. Outlook
Enhanced fast-ion transport can explain the apparent reduction in thermal confinement at high qmin • Compare two 2.6 actor matched 2.4 qmin~1 discharges: onfinement F 2.2 qmin ~ 1 & qmin ~ 2 2.0 1.8 qmin~2 H89 C 1.6 1.4 1.2 1.0 1.5 2.0 2.5 3.0 qmin
Enhanced fast-ion transport can explain the apparent reduction in thermal confinement at high qmin 2.6 • Compare actor power balance 2.4 qmin~1 in qmin ~ 2 shot: AE E ffect onfinement F 2.2 Classical vs. 2.0 D f =1.3 m 2 /s • Reduced fast- 1.8 ion stored qmin~2 H89 C 1.6 energy • Less power 1.4 delivered to 1.2 thermal plasma 1.0 1.5 2.0 2.5 3.0 qmin Thermal diffusivities like qmin ~1 discharge
Outline 1. AEs degrade fast-ion confinement in many steady-state scenario discharges 2. Degradation of fast-ion confinement can account for the overall degradation in global confinement 3. Physical mechanism of fast-ion transport: critical gradient behavior due to many wave- particle resonances 4. Outlook
Different combinations of on-axis & off-axis beams vary the fast-ion gradient that drives AEs CLAS S ICAL BE AM PR OFILE S 5 TY (10 12 cm -3 ) Use L-mode plasma in (On-axis) Beam Mix=0.0 #146102 @ 550 ms 0.22 current ramp: 4 0.45 • Low AE threshold 3 I 0.72 NS • Well diagnosed T-ION DE 1.0 (Off-axis) 2 1 AS F 0 On-axis injection 0.0 0.2 0.4 0.6 0.8 NOR MALIZE D MINORR ADIUS
As predicted by linear AE stability theory, a steeper gradient drives more AE activity CLAS S ICAL BE AM PR OFILE S 5 TY (10 12 cm -3 ) Beam Mix=0.0 #146102 @ 550 ms 0.22 4 0.45 3 I 0.72 NS T-ION DE 1.0 2 1.0 2.0 1 AS F 0 0.0 0.2 0.4 0.6 0.8 AEAmplitude NOR MALIZE D MINORR ADIUS 1.5 • Growth rate from TAEFL gyrofluid n=2 Growth rate 1.0 0.5 code n=3 Growth rate • GYRO gyrokinetic 0.5 code gives similar results 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 On axis Off axis BE AM MIX
Stronger AE activity causes a larger fast-ion deficit CLAS S ICAL BE AM PR OFILE S 5 TY (10 12 cm -3 ) Beam Mix=0.0 #146102 @ 550 ms 0.22 4 0.45 3 I 0.72 NS T-ION DE 1.0 2 1.0 2.0 1 AS F AEAmplitude Neutron/Classical 0 0.0 0.2 0.4 0.6 0.8 NOR MALIZE D MINORR ADIUS 1.5 • The measured neutron rate 1.0 0.5 approaches the classical prediction for off- 0.5 axis injection 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 On axis Off axis BE AM MIX
The measured fast-ion profile is nearly the same for all angles of injection! CLAS S ICAL BE AM PR OFILE S 5 TY (10 12 cm -3 ) Beam Mix=0.0 #146102 @ 550 ms 0.22 4 0.45 3 I 0.72 NS T-ION DE 1.0 2 1 AS F 0 0.0 0.2 0.4 0.6 0.8 Beam mix = 0.0 NOR MALIZE D MINORR ADIUS 0.45 0.72 3 • Suggests the fast-ion 1.0 transport is “stiff” FIDA Density • The linear stability 2 threshold acts (approximately) as a 1 “critical gradient” 0 Of course, in quiet plasmas, the 1.7 1.8 1.9 2.0 2.1 2.2 profiles differ. Major R adius (m)
A critical gradient model* reproduces the observed trend CLAS S ICAL BE AM PR OFILE S 0.8 5 TY (10 12 cm -3 ) Beam Mix=0.0 #146102 @ 550 ms 0.22 ATE 4 0.45 3 ONR I 0.72 NS T-ION DE 1.0 0.7 2 Theory UTR 1 AS F 0 0.0 0.2 0.4 0.6 0.8 D NE NOR MALIZE D MINORR ADIUS 0.6 MALIZE E xperiment 0.5 NOR 0.4 0.0 0.2 0.4 0.6 0.8 1.0 Off-axis On-axis BE AM MIX *Ghantous, Phys. Pl. 19 (2012) 092511. Gorelenkov TH/P1-2
Recent Data Supports Critical Gradient Model of Alfven Eigenmode (AE) Induced Fast Ion Transport • Beam power scan varies AE AE Power (a.u.) amplitude • Modulated off-axis beam allows measurement of incremental fast- SSNPA ~ Fast-ion Density ion flux P NBI-mod • Local fast-ion density ceases to rise above certain input power/ AE amplitudes – SSNPA Neutral particle analyzer -> fast- ion density localized in phase space
Above threshold, the modulated signal is strongly distorted by AE transport Classical ignal (a.u.) 0.05 2.1 MW(T otal P ower) Modulated S 9.3 MW 0.00 • Conditionally average the modulated signal -0.05 • At low power, the signal agrees P NBI-mod well with a classical model • Classically, the amplitude of the 0 10 20 30 40 50 TIME (ms) modulated signal should increase at high power
Infer the fast-ion transport from a continuity equation for the measured “density” Weight Function • Define a “density” that incorporates the phase-space sensitivity W in its definition Distribution Function “Flux” • Linearize. Obtain a continuity equation for 1 st order (modulated) quantities • When the AEs are absent, the transport term is negligible measure source in a low-power shot • With AEs, use the measured n to infer the divergence of the fast-ion flux
Divergence of fast-ion flux abruptly increases above an AE threshold critical gradient behavior 5 Amplitude AE Power (a.u.) AE 0 250 SSNPA ~ Fast-ion Density 200 Fast-Ion Div.Flux 150 100 50 0 -50 2 4 6 8 10 P NBI (MW)
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